No its not needed in your scenario.
taken from the GROW FAQ's
"CO2 can be a pain to manufacture safely, cheaply, and/or conveniently, and is expensive to set up if you use a CO2 tank system. CO2 is most usable for flowering, as this is when the plant is most dense and has the hardest time circulating air around its leaves. If your strictly growing vegetatively indoors, (transferring your plants outdoors to flower), then CO2 will not be a major concern unless you have a sealed greenhouse, closet or bedroom, and wish to increase yield and decrease flowering time."